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William is going to invest in an account paying an interest rate of 5.9% compounded
continuously. How much would William need to invest, to the nearest hundred
dollars, for the value of the account to reach $1,230 in 19 years?

Respuesta :

calculista

Answer:

[tex]\$400.92[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=19\ years\\ A=\$1,230\\ r=5.9\%=5.9/100=0.059[/tex]  

substitute in the formula above

[tex]1,230=P(e)^{0.059*19}[/tex]  

solve for P

[tex]1,230=P(e)^{1.121}[/tex]  

[tex]P=1,230/(e)^{1.121}[/tex]

[tex]P=\$400.92[/tex]  

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